Discontinuous Galerkin methods have become a powerful tool for approximation
the solution of compressible ﬂow problems. Their direct use for two-phase
ﬂow problems with phase transformation is not straightforward because
this type of ﬂows requires a detailed tracking of the phase front.
We consider the fronts in this contribution as sharp interfaces and
propose a novel multiscale approach. It combines an eﬃcient high-order
Discontinuous Galerkin solver for the computation in the bulk phases
on the macro-scale with the use of a generalized Riemann solver on
the micro-scale. The Riemann solver takes into account the eﬀects
of moderate surface tension via the curvature of the sharp interface
as well as phase transformation. First numerical experiments in three
space dimensions underline the overall performance of the method.